Question

prove that: PM=dRt
where,
p= atmospheric pressure(atm)
m= molar mass
d= density
R= ideal gas constant(0.0821)
t= temperature

Answer 1

pv=nrt
p=nrt/v 
we know n = m/M where m=mass, M=molar mass
p = mrt/Mv   we also know d = m/v
soo 
p= drt/M
re arranging this we get PM=drt

Answer 2

Proof for  PM=dRt:

Already we know that the Ideal Gas Equation is: PV=nRT

The ideal gas is also known as the general gas equation which is the state of 'hypothetical ideal gas'. It was first proposed by Emile Clapeyron. It was written as

PV=nRT

where  P, V and T are the pressure, volume and temperature. n is the 'number of moles' of gas and R is the 'ideal gas constant'.

If the number of moles is n=1, we get,  pV= RT

Now we are taking the value of n as $\frac {m}{M}$

Since $pV= \frac{mRT}{M}$

= $\frac {(mRT)}{VM}$

Since d= $\frac {m}{V}$

Then$p= \frac {(dRT)} {M}$

By rearranging the above we get

PM=dRt.

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